Adjusting Exponential Lévy Models Toward the Simultaneous Calibration of Market Prices for Crash Cliquets

24 Pages Posted: 28 Jul 2016

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Ajay Khanna

New York University (NYU)

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Date Written: July 28, 2016

Abstract

In this paper, option-calibrated exponential Lévy models are observed to typically overprice crash cliquets. Typical model Lévy tails are then not crash-market consistent. A general tail-thinning strategy is introduced that may be implemented on a class of parametric Lévy models closed under exponential tilting. Implementation on the Carr-Geman-Madan-Yor (CGMY) model leads to the CGAKMY model with a thinning function of (1 Α | χ |)-Κ. It is observed that this model adjustment can be crash market consistent.

Keywords: completely monotone function, Gauss Laguerre quadrature, gap risk pricing, beta exposure pricing, CGMY model, negative binomial process

Suggested Citation

Carr, Peter P. and Khanna, Ajay and Madan, Dilip B., Adjusting Exponential Lévy Models Toward the Simultaneous Calibration of Market Prices for Crash Cliquets (July 28, 2016). Journal of Computational Finance, 20(1), 89-111, DOI:10.21314/JCF.2016.309 . Available at SSRN: https://ssrn.com/abstract=2815431

Peter P. Carr

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Ajay Khanna

New York University (NYU) ( email )

Bobst Library, E-resource Acquisitions
20 Cooper Square 3rd Floor
New York, NY 10003-711
United States

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

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